AbstractLetFbe a number field, Supposex,y∈F* have the property that for alln∈Zand almost all prime ideals p of the ring of integers ofF* one has thatyn≡1 (modp) wheneverxn≡1 (modp). We show that thenyis a power ofx. This answers a question of Erdős. We also prove an elliptic analogue of this result
In this paper the family of elliptic curves over Q given by the equation y2 = (x + p)(x2 + p2) is st...
AbstractFor small odd primes p, we prove that most of the rational points on the modular curve X0(p)...
AbstractLet k be an algebraic number field and let θ be the ring of integers of k. We define for eac...
AbstractLetFbe a number field, Supposex,y∈F* have the property that for alln∈Zand almost all prime i...
AbstractIf A/K is an abelian variety over a number field and P and Q are rational points, the origin...
AbstractIn this paper we consider certain local–global principles for groups like S-units, abelian v...
AbstractLet A be an abelian variety over a number field K. If P and Q are K-rational points of A suc...
AbstractLetpbe an odd prime and Opbe the ring of integers in the cyclotomic fieldQ(ζ), whereζis a pr...
AbstractWe consider, for odd primes p, the function N(p, m, α) which equals the number of subsets S⊆...
AbstractIn this paper we consider orders of images of nontorsion points by reduction maps for abelia...
AbstractWe prove by the theory of algebraic numbers a result (Theorem 3) which, together with our ea...
The orders of the reductions of a point in the Mordell–Weil group of an elliptic curve by J. Cheon a...
Let $\{nP+Q\}_{n\geq0}$ be a sequence of points on an elliptic curve defined over a number field $K$...
AbstractThis paper continues the search to determine for what exponents n Fermat's Last Theorem is t...
AbstractLetkbe a number field and denote by okits ring of integers. Let p be a non-zero prime ideal ...
In this paper the family of elliptic curves over Q given by the equation y2 = (x + p)(x2 + p2) is st...
AbstractFor small odd primes p, we prove that most of the rational points on the modular curve X0(p)...
AbstractLet k be an algebraic number field and let θ be the ring of integers of k. We define for eac...
AbstractLetFbe a number field, Supposex,y∈F* have the property that for alln∈Zand almost all prime i...
AbstractIf A/K is an abelian variety over a number field and P and Q are rational points, the origin...
AbstractIn this paper we consider certain local–global principles for groups like S-units, abelian v...
AbstractLet A be an abelian variety over a number field K. If P and Q are K-rational points of A suc...
AbstractLetpbe an odd prime and Opbe the ring of integers in the cyclotomic fieldQ(ζ), whereζis a pr...
AbstractWe consider, for odd primes p, the function N(p, m, α) which equals the number of subsets S⊆...
AbstractIn this paper we consider orders of images of nontorsion points by reduction maps for abelia...
AbstractWe prove by the theory of algebraic numbers a result (Theorem 3) which, together with our ea...
The orders of the reductions of a point in the Mordell–Weil group of an elliptic curve by J. Cheon a...
Let $\{nP+Q\}_{n\geq0}$ be a sequence of points on an elliptic curve defined over a number field $K$...
AbstractThis paper continues the search to determine for what exponents n Fermat's Last Theorem is t...
AbstractLetkbe a number field and denote by okits ring of integers. Let p be a non-zero prime ideal ...
In this paper the family of elliptic curves over Q given by the equation y2 = (x + p)(x2 + p2) is st...
AbstractFor small odd primes p, we prove that most of the rational points on the modular curve X0(p)...
AbstractLet k be an algebraic number field and let θ be the ring of integers of k. We define for eac...
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